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lfunc_lfunctions • Show schema
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{'Lhash': '106145674889463053849809670979', 'a10': [0.0, 0.0], 'a2': [0.0, 5.414213562373095], 'a3': [0.0, 4.656854249492381], 'a4': [-21.31370849898476, 0.0], 'a5': [0.0, 0.0], 'a6': [-25.213203435596427, 0.0], 'a7': [0.0, -7.0], 'a8': [0.0, -72.08326112068524], 'a9': [5.31370849898476, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.325334251004612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 7.0]]]], 'bad_primes': [5, 7], 'central_character': '175.99', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '4781067255363082562054214130212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -5.414213562373095], [-8.0, 0]], [[1.0, 0], [0, -4.656854249492381], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.0]], [[1.0, 0], [52.254833995939045, 0], [1331.0, 0]], [[1.0, 0], [0, 30.65685424949238], [-2197.0, 0]], [[1.0, 0], [0, -37.22539674441618], 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'1.74516262062128442405345671298122', '2.66115853286060713733204180562753', '4.23483860846907235139540127449057', '5.52710301275790288475786828139895', '7.40419676289149172650288038103953', '8.566241642016171058844163407854388', '9.569119792558090229642504129007008', '10.60296608980760606100641000969594', '11.38757766780310008942033801105336'], 'prelabel': '2-175-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': 0.14758361765043326, 'root_number': '0.894427190999916 + 0.44721359549995787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0737918088252', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.083734173178597046867991202572', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.74516262062128442405345671298', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66115853286060713733204180563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.325334251004612, 'bad_primes': [5, 7], 'central_character': '5.4', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/4/b/c/99/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-175-5.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-175-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.083734173178597046867991202572', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '106145674889463053849809670979', 'Lhash_array': ['106145674889463053849809670979'], 'label': '2-175-5.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/4/b/c/99/4'}